Calculate to three significant digits the density of dinitrogen monoxide gas at exactly -15°C and exactly one atmosphere. You can assume dinitrogen monoxide gas behaves as an ideal gas under these conditions.
To solve this problem, we can use the ideal gas law:
PV = nRT
where:
P = pressure in atm
V = volume in L
n = number of moles
R = gas constant (0.0821 L·atm/(K·mol))
T = temperature in Kelvin
First, we need to convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = -15 + 273.15
T(K) = 258.15 K
Next, we know that the pressure is exactly one atmosphere:
P = 1 atm
The molar mass of dinitrogen monoxide (N2O) is 44.01 g/mol.
To find the number of moles, we'll use the molar mass and the ideal gas equation:
n = (m/M)
where:
m = mass in grams
M = molar mass in g/mol
Using the equation:
n = m/M
n = 44.01 g / 44.01 g/mol
n = 1 mol
Rounding to three significant digits, we have:
T = 258.15 K
P = 1 atm
n = 1 mol
V = unknown
Now we can rearrange the ideal gas law equation to solve for V:
V = (nRT) / P
V = (1 mol * 0.0821 L·atm/(K·mol) * 258.15 K) / 1 atm
V ≈ 21.17 L
Finally, we can calculate the density using the formula:
density = (mass) / (volume)
density = (m) / (V)
density = (44.01 g) / (21.17 L)
density ≈ 2.080 g/L
Therefore, the density of dinitrogen monoxide gas at exactly -15°C and exactly one atmosphere is approximately 2.080 g/L.